[Nexus 7 (2013) Q&A] 459below:
:victory: Look at that:

[433265.531574] usb 1-1.2: new high-speed USB device number 8 using dwc_otg
[433265.673304] usb 1-1.2: New USB device found, idVendor=058f, idProduct=6366
[433265.683227] usb 1-1.2: New USB device strings: Mfr=1, Product=2, SerialNumber=3
[433265.696306] usb 1-1.2: Product: Flash Card Reader/Writer
[433265.704789] usb 1-1.2: Manufacturer: Generic
[433265.712242] usb 1-1.2: SerialNumber: 058F63666438
[433265.740705] usb-storage 1-1.2:1.0: USB Mass Storage device detected
[433265.758190] scsi host0: usb-storage 1-1.2:1.0
[433266.852610] scsi 0:0:0:0: Direct-Access Multiple Card Reader 1.00 PQ: 0 ANSI: 0
[433266.883679] sd 0:0:0:0: Attached scsi generic sg0 type 0
[433267.216961] sd 0:0:0:0: [sda] 30212096 512-byte logical blocks: (15.5 GB/14.4 GiB)
[433267.252716] sd 0:0:0:0: [sda] Write Protect is off
[433267.260827] sd 0:0:0:0: [sda] Mode Sense: 03 00 00 00
[433267.269177] sd 0:0:0:0: [sda] No Caching mode page found
[433267.277833] sd 0:0:0:0: [sda] Assuming drive cache: write through
[433267.326702] sda: sda1 sda2 sda3 sda4 sda5 sda6 sda7 sda8 sda9 sda10 sda11 sda12 sda13 sda14 sda15 sda16 sda17 sda18 sda19 sda20 sda21 sda22 sda23 sda24 sda25 sda26 sda27 sda28 sda29 sda30
[433267.407314] sd 0:0:0:0: [sda] Attached SCSI removable disk
[root@lingua ~]# fdisk -l /dev/sda
Disk /dev/sda: 14.4 GiB, 15468593152 bytes, 30212096 sectors
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: gpt
Disk identifier: 98101B32-BBE2-4BF2-A06E-2BB33D000C20

Device Start End Sectors Size Type
/dev/sda1 131072 306143 175072 85.5M Microsoft basic data
/dev/sda2 393216 399359 6144 3M unknown
/dev/sda3 399360 405503 6144 3M unknown
/dev/sda4 524288 554287 30000 14.7M Linux filesystem
/dev/sda5 655360 656919 1560 780K unknown
/dev/sda6 656920 658479 1560 780K unknown
/dev/sda7 786432 787991 1560 780K unknown
/dev/sda8 787992 794135 6144 3M unknown
/dev/sda9 917504 920503 3000 1.5M unknown
/dev/sda10 920504 923503 3000 1.5M unknown
/dev/sda11 923504 927599 4096 2M unknown
/dev/sda12 927600 937839 10240 5M unknown
/dev/sda13 937840 938863 1024 512K unknown
/dev/sda14 1048576 1081343 32768 16M unknown
/dev/sda15 1179648 1180671 1024 512K unknown
/dev/sda16 1180672 1180673 2 1K unknown
/dev/sda17 1180674 1183673 3000 1.5M unknown
/dev/sda18 1183674 1187769 4096 2M unknown
/dev/sda19 1187770 1198009 10240 5M unknown
/dev/sda20 1198010 1199033 1024 512K unknown
/dev/sda21 1199034 1200057 1024 512K unknown
/dev/sda22 1310720 3031039 1720320 840M Linux filesystem
/dev/sda23 3031040 4177919 1146880 560M Linux filesystem
/dev/sda24 4194304 4196351 2048 1M unknown
/dev/sda25 4325376 4345855 20480 10M unknown
/dev/sda26 4456448 4456463 16 8K unknown
/dev/sda27 4456464 4456479 16 8K unknown
/dev/sda28 4456480 4456481 2 1K unknown
/dev/sda29 4587520 4587583 64 32K unknown
/dev/sda30 4718592 30212062 25493471 12.2G Linux filesystem

I succeeded in reballing the Kingston eMMC and soldering it onto one of those eMMC to USB devices. I went on to dump all the partitions for safekeeping. My next course of action is going be the soldering of the new eMMC onto the N7 motherboard.

/edit

The Kingston eMMC behaves exactly the same as to when it still was attached to the N7. It is capable of reading, but when a write is requested the whole thing just freezes up.